Why Would that be the case? 
They are a non native invasive species and they carry squirrel pox.
Greys are fairly immune to the virus, however our native red squirrel is not and they succumb to it, greys have wiped out the native red squirrel population over vast areas of the UK
They are bigger, heavier and carry this virus, that means they out compete the smaller more specialist reds for food as well which is also an issue.
They do immense damage to trees, especially younger trees, Oak and beech are particularly vulnerable to attack, the grey will strip the bark from bottom to top of trees up to 20yo, ive seen them do this in person, they do it in the spring time especially as they want the sap that is rising, its sweet and they get addicted to it, almost pissed on it, as the bark is removed the tree bleeds and they drink that sap.
They cost the forests industry in this country hundreds of thousands in damages, they take insulation of pipes in lofts and will take the insulation off electric cables, grey squirrel damage has caused fires in buildings due to this.